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Equations of state of hydrodynamic type and particle statistics of a Dyson gas in an analytic confining potential

  • Antonio Moro
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Abstract

We investigate the equilibrium thermodynamics of a Dyson gas in connection with a set of integrable statistical mechanical observables satisfying the Toda Lattice hierarchy. We prove that in the thermodynamic limit, the integrable observables are state functions satisfying a set algebraic equations of state in closed form, obtained from direct integration of the Toda Lattice hierarchy in the continuum limit. We then explore the connection between regularity and critical behaviour of the state functions and the Dyson gas particle statistics via Monte Carlo simulations. We show that the properties of the integrable observables, such as regularity, multivaluedness, cusp singularities, carry information on the macroscopic particle statistics and its qualitative changes but with some limitations.

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Cite

BibTeXRIS
BibTeX
@misc{moro2026equations,
  title = {{Equations of state of hydrodynamic type and particle statistics of a Dyson gas in an analytic confining potential}},
  author = {Antonio Moro},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.23795},
  eprint = {2609.23795},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.23795},
}
RIS
TY  - UNPB
TI  - Equations of state of hydrodynamic type and particle statistics of a Dyson gas in an analytic confining potential
AU  - Antonio Moro
PY  - 2026
DA  - 2026/09/20
PB  - arXiv
DO  - 10.48550/arxiv.2609.23795
UR  - https://arxiv.org/abs/2609.23795
AB  - We investigate the equilibrium thermodynamics of a Dyson gas in connection with a set of integrable statistical mechanical observables satisfying the Toda Lattice hierarchy. We prove that in the thermodynamic limit, the integrable observables are state functions satisfying a set algebraic equations of state in closed form, obtained from direct integration of the Toda Lattice hierarchy in the continuum limit. We then explore the connection between regularity and critical behaviour of the state functions and the Dyson gas particle statistics via Monte Carlo simulations. We show that the properties of the integrable observables, such as regularity, multivaluedness, cusp singularities, carry information on the macroscopic particle statistics and its qualitative changes but with some limitations.
ER  -